Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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            <s xml:id="echoid-s8249" xml:space="preserve">
              <pb o="219" file="0257" n="257" rhead="Conicor. Lib. VI."/>
            dem nulla ratione rectæ lineæ inter ſe æquidiſtantes, inter curuas interceptæ de-
              <lb/>
            terminare poſſunt prædictarum curuarum diſtantias; </s>
            <s xml:id="echoid-s8250" xml:space="preserve">quandoquidem inæquali-
              <lb/>
            ter ſemper inclinantur ad quamlibet prædictarum curuarum, & </s>
            <s xml:id="echoid-s8251" xml:space="preserve">rectæ lineæ in-
              <lb/>
            terceptæ, quæ ſunt perpendiculares ad vnam ipſarum, non erunt inter ſe æqui-
              <lb/>
            diſtantes. </s>
            <s xml:id="echoid-s8252" xml:space="preserve">Et quia, vt dictum eſt, prædictæ perpendiculares ſunt diſtantiarum
              <lb/>
            legitimæ menſuræ, nunquàm concludi poteſt certo, quod prædictæ ſectiones ſint
              <lb/>
            æquidiſtantes. </s>
            <s xml:id="echoid-s8253" xml:space="preserve">vel ſibi ipſis ſucceſſiuè viciniores ſiant, niſi conſiderentur rectæ
              <lb/>
            lineæ interceptæ ad vnam ſectionum perpendiculares: </s>
            <s xml:id="echoid-s8254" xml:space="preserve">quod quidem hucuſque
              <lb/>
            quod ſciam factum non eſt, neque forſan huiuſmodi ſpeculatio inuentu facilis
              <lb/>
            erit, aut iniucunda.</s>
            <s xml:id="echoid-s8255" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8256" xml:space="preserve">In parabola, vel hyperbola A B C ad eius axim E A I ducere ra-
              <lb/>
              <note position="right" xlink:label="note-0257-01" xlink:href="note-0257-01a" xml:space="preserve">PROP. 6.
                <lb/>
              Addit.</note>
            mum breuiſſimum æquidiſtantem alicui rectæ lineæ E F, quæ oportet,
              <lb/>
            vt efficiat cum axi ad partes ſectionis angulum A E F acutum, ſed in
              <lb/>
            hyperbola ſit minor ſemiße vnius recti, & </s>
            <s xml:id="echoid-s8257" xml:space="preserve">angulus F E X ab vna
              <lb/>
            asymptoto, & </s>
            <s xml:id="echoid-s8258" xml:space="preserve">recta linea E F contentus ſit acutus.</s>
            <s xml:id="echoid-s8259" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8260" xml:space="preserve">Fiat angulus A E D æqualis an-
              <lb/>
              <figure xlink:label="fig-0257-01" xlink:href="fig-0257-01a" number="298">
                <image file="0257-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-01"/>
              </figure>
            gulo A E F, & </s>
            <s xml:id="echoid-s8261" xml:space="preserve">ex vertice A du-
              <lb/>
            catur recta linea A B efficiens an-
              <lb/>
            gulum I A B, qui ſimul cum an-
              <lb/>
            gulo A E F vnum rectum angulũ
              <lb/>
            compleat; </s>
            <s xml:id="echoid-s8262" xml:space="preserve">ſed in hyperbola, quia
              <lb/>
            vterq; </s>
            <s xml:id="echoid-s8263" xml:space="preserve">angulus X E A, & </s>
            <s xml:id="echoid-s8264" xml:space="preserve">A E F
              <lb/>
            deficit à ſemirecto erũt ambo mino-
              <lb/>
            res ſumma præcedentium, ſcilicet
              <lb/>
            vno angulo recto; </s>
            <s xml:id="echoid-s8265" xml:space="preserve">ergo ablato cõmuni
              <lb/>
            angulo A E F, erit angulus I A B
              <lb/>
            maior angulo A E X. </s>
            <s xml:id="echoid-s8266" xml:space="preserve">Poſtea, quia
              <lb/>
            tam A E F, quàm A E D minor eſt ſemiſſe vnius anguli recti, & </s>
            <s xml:id="echoid-s8267" xml:space="preserve">A E F cum
              <lb/>
            angulo I A B vnum rectum angulum complent; </s>
            <s xml:id="echoid-s8268" xml:space="preserve">ergo angulus I A B maior erit
              <lb/>
            angulo D E A: </s>
            <s xml:id="echoid-s8269" xml:space="preserve">& </s>
            <s xml:id="echoid-s8270" xml:space="preserve">propterea recta linea A B producta neceſſario ſecabit vtram-
              <lb/>
            que rectam lineam E D, & </s>
            <s xml:id="echoid-s8271" xml:space="preserve">E X asymptotum extra ſectionem cadentem ad par-
              <lb/>
            tes D, X; </s>
            <s xml:id="echoid-s8272" xml:space="preserve">ideoque A B hyperbolen ſecabit in aliquo alio puncto B. </s>
            <s xml:id="echoid-s8273" xml:space="preserve">In parabola
              <lb/>
            verò, quia recta linea A B axim
              <lb/>
              <figure xlink:label="fig-0257-02" xlink:href="fig-0257-02a" number="299">
                <image file="0257-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-02"/>
              </figure>
            ſecat in vertice A non ad angulos
              <lb/>
            rectos (cum anguli I A B, & </s>
            <s xml:id="echoid-s8274" xml:space="preserve">A
              <lb/>
              <note position="right" xlink:label="note-0257-02" xlink:href="note-0257-02a" xml:space="preserve">17. 27.
                <lb/>
              lib. I.</note>
            E F rectum compleant) ergo A B
              <lb/>
            ſectioni occurrit in duobus pun-
              <lb/>
            ctis. </s>
            <s xml:id="echoid-s8275" xml:space="preserve">Secetur iam A B bifariam
              <lb/>
            in L, & </s>
            <s xml:id="echoid-s8276" xml:space="preserve">per L ducatur diameter
              <lb/>
            ſectionis L G ſectioni occurrens in
              <lb/>
              <note position="right" xlink:label="note-0257-03" xlink:href="note-0257-03a" xml:space="preserve">35. 36.
                <lb/>
              lib. I.
                <lb/>
              5. lib. 2.</note>
            G, & </s>
            <s xml:id="echoid-s8277" xml:space="preserve">per G ducatur contingens G
              <lb/>
            H, ſeu parallela A B ſecans axim
              <lb/>
            in H, & </s>
            <s xml:id="echoid-s8278" xml:space="preserve">per G ducatur I G O per-
              <lb/>
            pendicularis ad G H. </s>
            <s xml:id="echoid-s8279" xml:space="preserve">Dico I G
              <lb/>
            problema efficere. </s>
            <s xml:id="echoid-s8280" xml:space="preserve">Quoniam </s>
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